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3 years ago

What number must be added to the expression below to complete the square?

Mathematics

2 answers:

DedPeter [7]3 years ago

8 0

Answer:

1/4

Step-by-step explanation:

To complete the square, use the formula (b/2)^2

The Quadratic Formula is: a+bx+c

thus a = x^2, b = -1

You then plug in the numbers in the formula above

(b/2)^2 = (-1/2)^2 = (1/2)^2 =1/4

stiv31 [10]3 years ago

7 0

D. 1/4

Explanation:

a perfect square is written in the form

$(x+a)^2 = x^2 + 2ax +a^2$ (1)

In our problem, we have this perfect square:

$x^2 - x + C$ (2)

with C being unknown. However, by comparing (1) and (2), we know that

$2a=-1$

So, we find

$a=-\frac{1}{2}$

and therefore, the missing term must be

$a^2 = \frac{1}{4}$

so the complete square is

$x^2 -x +\frac{1}{4}$

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What is the distance between (1,-5) and (-3,6)

Wewaii [24]

Answer:

$\large\boxed{\sqrt{137}\approx11.7}$

Step-by-step explanation:

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

We have two points (1, -5) and (-3, 6). substitute:

$d=\sqrt{(-3-1)^2+(6-(-5))^2}=\sqrt{(-4)^2+11^2}=\sqrt{16+121}=\sqrt{137}$

4 0

3 years ago

Question is attached answer asap. Will give brainliest

schepotkina [342]

1.) (-2,3)
2.) a=175/43 b= -70/43
3.)(7,3)

I believe i am right
I haven't one this in a long time
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6 0

3 years ago

A particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls invol

Phoenix [80]

Answer:

0.1091 or 10.91%

Step-by-step explanation:

We have been given that a particular telephone number is used to receive both voice calls and fax messages. suppose that 20% of the incoming calls involve fax messages and consider a sample of 20 calls. We are asked to find the probability that exactly 6 of the calls involve a fax message.

We will use Bernoulli's trials to solve our given problem.

$P(X=x)=^nC_x\cdot P^x(1-P)^{n-x}$

$P(X=6)=^{20}C_6\cdot (0.20)^6(1-0.20)^{20-6}$

$P(X=6)=\frac{20!}{6!(20-6)!}\cdot (0.20)^6(0.80)^{14}$

$P(X=6)=\frac{20!}{6!(14)!}\cdot (0.000064)(0.04398046511104)$

$P(X=6)=38760\cdot (0.000064)(0.04398046511104)$

$P(X=6)=0.1090997009730$

$P(X=6)\approx 0.1091\\$

Therefore, the probability that exactly 6 of the calls involve a fax message would be approximately 0.1091 or 10.91%.

4 0

3 years ago

7. The length of a minute hand of a clock is 3.5cm. Find the angle it turns through if it

babymother [125]

Answer:

The angle it turns through if it sweeps an area of 48 cm² is 448.8°

Step-by-step explanation:

If the length of a minute hand of a clock is 3.5cm, to find the angle it turns through if it sweeps an area of 48 cm, we will follow the steps below;

area of a sector = Ф/360 × πr²

where Ф is the angle, r is the radius π is a constant

from the question given, the length of the minute hand is 3.5 cm, this implies that radius r = 3.5

Ф =? area of the sector= 48 cm² π = $\frac{22}{7}$

we can now go ahead to substitute the values into the formula and solve Ф

area of a sector = Ф/360 × πr²

48 = Ф/360 × $\frac{22}{7}$ × (3.5)²

48 = Ф/360 × $\frac{22}{7}$ ×12.25

48 = 269.5Ф / 2520

multiply both-side of the equation by 2520

48×2520 = 269.5Ф

120960 = 269.5Ф

divide both-side of the equation by 269.5

448.8≈Ф

Ф = 448.8°

The angle it turns through if it sweeps an area of 48 cm² is 448.8°

7 0

3 years ago

12% of children are nearsighted, but this condition often is not detected until they go to kindergarten. A school district tests

Klio2033 [76]

Answer:

There is a 34.60% probability that 0 or 1 of them is nearsighted.

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are nearsighted, or they are not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we have that:

12% of children are nearsighted. This means that $p = 0.12$ .

A school district tests all incoming kindergarteners' vision. In a class of 18 kindergarten students, what is the probability that 0 or 1 of them is nearsighted?

There are 18 students, so $n = 18$